Study area

The study area comprises the Rural Development District of Toluca (DDRT), one of the eight DDRs in the State of Mexico. It is located in the center-east of the State of Mexico between the parallels 19° 00’ and 19° 35’ north latitude and between the meridians: 99° 54’ and 99° 14’ west longitude, with altitudes between 1 800 and 4 640 masl (^{Granados and Sarabia, 2013}). It has an area of 302 604 ha and is made up of 24 municipalities. It is characterized by its fertile valleys with deep soils (Figure 1). The research work was carried out during the spring-summer (S-S) agricultural cycle of 2019.

Figure 1 Geographical location of the Rural Development District of Toluca. 

In the DDRT, 132 784.9 ha are cultivated under rainfed conditions (Table 1), and it contributes on average 22% of the volume of corn production in the state; however, in this region there are more than 100 days with frosts per year, influenced by the altitude, which leads to recurrent frosts that affect corn production in this region. In order of importance, the municipalities that report the largest area sown with rainfed corn in the DDRT are Almoloya de Juárez, Toluca, Zinacantepec, Tenango del Valle, Lerma and Temoaya (^{SIAP, 2014}), as shown in Table 1.

Frost period

To identify the frosts that occurred in the DDRT in the cycle (S-S) and that affect the vegetative cycle of corn, the year 2019 was taken as a sample, which was a year with records of more frosts verified through previous bibliographic research and the analysis of climate data.

Considering that corn is susceptible to a wide range of temperatures between 5 and 45 °C and that, below 4 °C, temperatures can cause damage to the crop (^{Mondragón, 2005}). When the temperature of the plant reaches temperatures of the freezing point of the water, it causes ice crystals intracellularly in the tissues, causing cell death, wilting, dehydrated reproductive organs, sucked grains, flaccidity of fruits and even a possible death of the plant (^{FAO, 2010}).

To identify minimum temperatures less than or equal to 4 °C, since below that value they affect rainfed corn, the daily minimum temperatures below 4 °C during the May-October period were analyzed, whose data were obtained from 20 weather stations located in the study area (^{CLICOM, 2019}). Interpolations were then performed using the inverse distance weighted (IDW) method at a power of value 2, a deterministic distance-weighting procedure. The interpolation of the problem point is done by assigning weights to the data in the environment in inversely function of the distance that separates them Inverse Distance Weighting (IDW). This procedure was performed from the ArcGis 10.4^® software platform.

Crop monitoring through vegetation indices

The monitoring of the corn was performed from the growth stage to physiological maturity based on the normalized difference vegetation index (NDVI) obtained through multitemporal analysis of MODIS/Terra satellite images. With the increasing and decreasing values of this index, the areas affected by some anomaly, mainly by frosts, were identified. The relationship between the NDVI and the vegetative development phases of corn is high (Soria and Granados, 2005). The S-S agricultural cycle of corn in this region occurs from May to October with different phases of growth: a) growth and development, whose NDVI values increase; b) flowering and grain filling, with greater plant vigor and NDVI values greater than 0.6; and c) physiological maturity and senescence, whose NDVI levels decrease rapidly (Figure 2).

Figure 2 Relationship of the NDVI and the phases of vegetative development of corn in the Toluca valley. 

When vegetation suffers some type of stress such as summer water deficit or frosts, its reflectance will be lower in the near-infrared and red region of the electromagnetic spectrum. The greater the contrast of the reflectances between the infrared and red bands, the greater the vegetal vigor of corn. The low values of this relationship indicate a diseased or senescent vegetation, until reaching covers without vegetation such as bare soil that reports indices close to zero (^{Soria et al., 1998}).

The NDVI registers values between -1 and 1 and is the most widely used in agronomic applications (^{Granados et al., 2004}). An NDVI value of 0.1 can be set as the critical threshold for vegetation covers and 0.5 for dense and healthy vegetation. MODIS/Terra images have a temporality of 16 days and a spatial resolution of 250 m. In the present study, scenes from the May-October 2014 period that covered the entire DDRT were analyzed. For the extraction of the NDVI from these images, the ENVI-Ver. 5.1^® software was used, using the following expression: NDVI=R Nir - R RedR Nir + R Red Where: R_Nir reflectances of radiation in the near infrared of the spectrum and R_Red reflectances of the radiation of the visible red of the spectrum.

By means of map algebra procedures, by superimposing and comparing the maps of minimum temperature (T< 4 °C) with the maps of NDVI, it was possible to identify the areas affected by frosts that damaged the cultivation of rainfed corn.

Corn area affected by frosts

To quantify the corn area affected by frosts in the S-S 2014 agricultural cycle, the analysis was carried out in two stages (before and after the event). The procedure consisted of the following: six images of 2019 from the Landsat-8 satellite Operational Land Imager (OLI) were selected, with a percentage of cloudiness less than 15% (^{USGS, 2019}) with a temporal resolution of 16 days, and a spatial resolution of 15 m (Table 2). These images were managed from the platform Landsatlook.usgs.gov/viewer, which were subjected to geometric, radiometric and atmospheric correction processes through the ENVI^® processor. Next, mosaics of the previously grouped scenes were generated for analysis (before and after the event). A false-color (RGB) band combination was obtained to highlight the traits of the corn plots and achieve a better discrimination of the crop.

To determine the cultivated area of corn, the images were subjected to a supervised classification process, which consists of an ordering of the pixels in a finite number of classes or categories, based on the values of digital levels, a procedure that uses the radiometric intensity of each pixel. Polygons known as training camps were previously selected and digitized. Then the maximum likelihood algorithm (maximum likelihood classification) was used. From the classification resulting from the two periods, the cultivated area (hectares) and the spatial distribution of the corn cultivation before and after frost were obtained. The change in corn cover in two vegetative cycles was then estimated using the Thematic Change Workflow tool of ENVI^®.

Spatial analysis of the corn area affected by frosts

To explain the spatial relationships between the affected corn area and the environmental variables that have the greatest influence on the manifestation of a frost, an explanatory model was generated using geostatistical methods of regression at the pixel level, as well as GIS tools. To do this, the loss of corn cover (affected corn area), as a dependent variable, and five independent or explanatory variables were used: climatic (minimum temperature, frequency of cold days and precipitation) and environmental (digital elevation model and slope of the terrain) (Table 3).

Temperature and precipitation data were obtained from the record of 20 weather stations distributed in the study area (^{Clicom, 2019}). To calculate the minimum temperatures, daily values of ≤4 °C were extracted from the database, which were averaged per month during the May-October period in the S-S 2019 cycle. From the result of this procedure, the number of times the frost event occurred (T≤ 4 °C) on a monthly basis was estimated, and thus obtain the frequency of cold days. The monthly accumulated rainfall was obtained from the climatological database (^{Clicom, 2019}) for the same period May-October.

The results of these three variables (minimum temperature, frequency of cold days and precipitation) were interpolated using the IDW method. The digital elevation model was obtained directly from the ^{INEGI (2017)} platform, and the slope map of the terrain was derived from this product. To perform these processes, the ArcGis^® Software was used. All variables were standardized to the UTM projection system with WGS84 datum and converted to raster format.

Frost occurrence probability map

The probability of frost occurrence in the DDRT for the year 2019 was obtained from a multiple linear regression (MLR) model with the ‘Multireg’ tool of the TerrSet software, where the coefficients of each explanatory variable (regression equation) were estimated, and in conjunction with the covers of the values of the dependent and explanatory variables, using a raster calculator, the probability map was obtained, which represents the probability that a pixel occupied by corn is lost due to the effect of frosts. Of the resulting values, ranges (low, medium, high and very high) were assigned.

Period of frosts that affect the cultivation of corn

Figure 3 shows the maps of the monthly minimum temperatures (<4 °C) for the period from May to October 2019, the same period that corresponds to the vegetative cycle of corn. It is observed that the months where temperatures below the critical threshold that affected the growth and development and corn (<4 °C) were recorded were May and August, with more than 40% of the territory of the study area, mainly in hillside areas. In October, the largest affected area was recorded, with temperatures below 0 °C in the mountain areas that correspond to the west, northwest and southwest region of the study area.

Figure 3 Behavior of the minimum temperature from May to October in the DDRT. 

The monthly minimum temperatures values (<4 °C) recorded in the study area significantly affected the cultivation of corn, mainly in the growth stage in some areas. In other areas, frosts coincided with the flowering and grain filling stage, a stage in which the plant is more sensitive to frost damage, affecting its productivity (^{Barrales et al., 2002}). When comparing Figures 3 and 4, we found that the largest area with temperatures below 4 °C, which were recorded in May, August and October, these coincide with the stages of emergence, flowering and physiological maturity of corn (^{Granados and Sarabia, 2013}), where those recorded in August could cause more damage since the corn was in the flowering stage.

Figure 4 Behavior of the phenological stages of corn in the Toluca Valley. 

Vegetation index and crop vigor (NDVI)

Climate variability can be obtained by means of remote sensing tools, for the understanding of the phenology of ecosystems based on the temporal variation of vegetation greenness (^{Gómez, 2013}), therefore, continuous monitoring of the total cultivated area of corn was carried out based on the normalized difference vegetation index (NDVI), through the multitemporal analysis of MODIS/Terra satellite images with a frequency of 16 days during the May-October period, where the effect of low temperatures that caused temporary wilting to the foliage of the corn in the S-S 2019 agricultural cycle was observed.

As shown in Figure 5, the values of the NDVI that indicates the greenness index; with the map algebra it was possible to identify the dynamics of the behavior of this variable, since it increases in the first half of September and subsequently descends in the second half of the same month, which is combined with the presence of temperatures below 4 °C affecting the agricultural area of the municipalities of Almoloya de Juárez, Zinacantepec, south and north of Toluca, Temoaya, Huixquilucan, Calimaya and Tenango del Valle.

These months are decisive for the good development of corn, where the maximum growth and vegetative development are expressed in August (flowering and grain filling), and it is where maximum NVDI values were obtained.

Figure 5 Behavior of the NDVI at the biweekly level in the cultivated areas of corn. 

One of the advantages of crop monitoring through the NDVI, which indicates the greenness index or degree of health of the crops, is that they can identify anomalies in the foliage of the plants. In this case, a sudden decrease in low levels of corn greenness in the study area was identified. By superimposing the maps of NDVI (Figure 3) and monthly minimum temperatures below 4 °C (Figure 5), it was possible to identify that there is a close relationship between these two variables.

Corn area affected by frosts

Before the frost, the corn area to July was 126 500.7 ha and after the frost (August-September), the area decreased to 122 989.15 ha, a reduction of 3 511.6 ha, which represents 2.77% (Figure 6).

Figure 6 Cultivated area of corn before and after frosts. 

The municipalities that reported the largest area affected by frosts were the following: Almoloya de Juárez with 32%, Zinacantepec with 18% and Tenango del Valle with 9.4%. With smaller affected areas and reporting lower values of 0.5% were Capulhuac, Otzolotepec, Xonacatlán, San Antonio la Isla, Mexicaltzingo, Atizapán, Chapultepec, Texcalyacac and San Mateo Atenco (Table 4).

Frost-area of corn affected relationship

When applying the multiple linear regression (MLR) model, it was found that some variables have a greater influence on the manifestation of frosts (^{Eastman, 2015}) and as observed in Table 5, altitude has a greater influence on the occurrence of frosts, followed by precipitation and minimum temperature. With less association value are the slope of the terrain and the frequency of cold days.

All variables have a positive relationship, this means that, with higher altitude, less rain, greater number of days with minimum temperature, greater slope and frequency of cold days, there are more probabilities of frost occurrence.

Frost risk probability map

With the RLM model, the coefficients of each explanatory variable were estimated, and by the relationship between a dependent variable (frost) and a set of independent variables (the variables that cause a frost): climatic and environmental (^{Pineda et al., 2010}). The risk probability map indicates the probability that a minimum area of corn represented on the map (pixel) will be lost because of frosts (Figure 7). Of the total area that is lost due to frosts, the probability obtained is: with low risk 96%, medium risk 2%, high risk 2% and with very high risk 0.3%.

Figure 7 Spatial distribution of the risk of frost occurrence in the DDRT. 

The risk levels for each of the 24 municipalities that make up the DDRT are shown in Table 6, where it is observed that the municipalities with the largest area are: Almoloya de Juárez with 1 132 ha (32.2%), Zinacantepec with 618 ha (17.6%), Tenango del Valle with 331 hectares (9.4%) and Santiago Tianguistenco with 249 ha (7.1%). Together, these municipalities represent more than half of the area with a probability of corn loss due to frosts.

The only municipality where there is no risk of frosts is San Mateo Atenco. Those municipalities with high and very high risk make up an area of 65 ha; that is; 1.8% of the total estimated corn area in 2019, which are located in the center and northwest of Almoloya de Juárez, north of Temoaya and east of Lerma (Figure 7). Municipalities with different levels of frost risk are shown in Table 6.